Abstract

In this article we study stability properties of gO, the standard Green kernel for O an open regular set in ℝd. In d ≥ 3 we show that gOβ is again a Green kernel of a Markov Feller process, for any power β ∈ [1,d/(d − 2)). In dimension d = 2, we show the same result for gOβ, for any β ≥ 1 and for kernels exp(αgO),exp(αgO)−1, for α ∈ (0,2π), when O is an open Greenian regular set whose complement contains a ball.